How do I fix this weird material/ texture of the glass?
The lower faces of the liquid are interfering with the lower faces of the inside of the cup. You can fix this by scaling the liquid in the Z axis so that these lower faces are a little above the lower inner faces of the cup.
To do this:

Select the Liquid object and in Edit mode with Face select mode active, select the face in the middle of the top face of the Liquid.

With the keyboard shortcut Shft + S choose the  Cursor to Selected option.

In the Header change the Pivot Point to 3D Cursor (see screenshot below).




Still in Edit mode select All of the Liquid object.
Now scale a little along the Z axis so that the bottom of the liquid is not touching the bottom of the cup.

Tab out of edit mode and try a render :